1. Field of the Invention
The invention relates to a method for direct measurement of the mixed-mode scattering matrix with a vectorial network analyzer (also referred to below as VNA).
2. Discussion of the Background
Lines conventionally used for the transmission of electrical signals generally comprise two separate conductors. In the past, these lines were generally unbalanced, that is to say, one conductor is disposed at earth or ground potential. With an earthed, unbalanced line, only one wave mode is generally capable of propagation. More recently, however, signals have also increasingly been transmitted via balanced-to-earth lines. In a balanced-to-earth line, also referred to as a balanced line, both conductors are detached from the ground potential. Accordingly, two fundamental modes are capable of propagation, namely the differential mode and the common mode. In the differential mode, which is preferred for signal transmission, the earthed signal voltages of the two conductors have the same amplitude but opposing phases. By contrast, in the common mode, not only the amplitudes but also the phases of the earthed, single-conductor modes are the same. Each physically-possible wave mode can be described as a linear combination of differential mode and common mode.
By comparison with that of earthed signals, the transmission of differential-mode signals has the advantages that, on the one hand, any interference signals, which may be present in the earth, are not added to the useful signal, from which they can no longer be separated, and, on the other hand, because of its symmetry, the line radiates a small interference-signal field. In view of the increasing spread of differential-mode transmission, electrical components with balanced ports are increasingly manufactured.
It is conventional to use network-analyzers to measure the electrical properties of components at higher frequencies. The primary test parameters of network analyzers are scattering (S-) parameters, which describe the transmission and reflection behaviour of a component, which will be referred to below as the device under test (MO). A vectorial network analyzer (VNA) provides the S-parameters as complex values, that is to say, with modulus and phase information. The complex S-parameters can be converted into further descriptive parameters of the device under test (MO), for example, Z-parameters, Y-parameters or group delay time.
However, commercially-available vectorial network analyzers have at their disposal only unbalanced (also referred to as nodal) test ports, to which the balanced ports of a device under test (MO) cannot be connected directly. It is therefore conventional to connect each of the two poles of a balanced device port to the pole conducting the signal voltage, that is to say, generally, to the inner coaxial conductor of an unbalanced VNA test port. Provided the device under test (MO) behaves in a linear manner, it is possible to measure the unbalanced S-parameters of the device under test (MO) with the unbalanced VNA, and then to convert these into balanced S-parameters. A conversion process of this kind is described in the specialist article by D. E. Bockelman, W. R. Eisenstadt: “Combined Differential and Common-Mode Scattering Parameters: Theory and Simulation”, IEEE Transactions on Microwave Theory and Techniques, Volume 43, No. 7, July 1995, pp. 1530-1539. The S-parameters of a device under test (MO), which provides balanced ports, are also described as mixed-mode parameters. This description results from the fact that the scattering matrix of a device under test with balanced ports describes the transmission between incoming and outgoing differential-mode and common-mode waves. If unbalanced ports are added, the transmission functions between three different modes are contained in the mixed-mode S-matrix. For example, the mixed-mode S-matrix SM of a filter with unbalanced input at port 1 and balanced output at port 2 provides the 9 elements presented below:
                              s          M                =                  (                                                                      s                                      ss                    ⁢                                                                                  ⁢                    11                                                                                                s                                      sd                    ⁢                                                                                  ⁢                    12                                                                                                s                                      sc                    ⁢                                                                                  ⁢                    11                                                                                                                        s                                      ds                    ⁢                                                                                  ⁢                    21                                                                                                s                                      dd                    ⁢                                                                                  ⁢                    22                                                                                                s                                      d                    ⁢                                                                                  ⁢                    c                    ⁢                                                                                  ⁢                    22                                                                                                                        s                                      cs                    ⁢                                                                                  ⁢                    21                                                                                                s                                      c                    ⁢                                                                                  ⁢                    d                    ⁢                                                                                  ⁢                    22                                                                                                s                                      cc                    ⁢                                                                                  ⁢                    22                                                                                )                                    (        1        )            The element index s (single ended) denotes the unbalanced mode of port 1; d (differential) denotes the differential-mode and c (common) denotes the common mode of port 2.
Active devices under test with balanced ports, such as differential-mode amplifiers, can provide nonlinear behaviour. In this case, the transmission functions for common-mode waves and differential-mode waves cannot be obtained by linear superposition of the transmission functions for unbalanced waves. On the contrary, for devices under test of this kind, appropriate VNAs must be capable of generating a genuine balanced excitation signal (stimulus signal).
A VNA for devices under test with two balanced ports is disclosed, for example, in the U.S. Pat. No. 5,495,173 B1. In this context, the device under test is supplied alternately in the transmission and reflection direction with a differential-mode and a common-mode generator signal. These signals are generated using hybrid circuits. The disadvantage in this context is that maintaining the amplitude and phase conditions for pure differential-mode and common-mode signals is dependent upon the ideality of the hybrid circuits. Sufficiently-good properties can be realized with circuits of this kind only over a relatively-limited frequency range, wherein a maximum ratio between the lower and upper frequency limit of approximately 1:8 can be achieved. Furthermore, all of the circuit components behind the hybrids must provide the most identical transmission behaviour possible, so that the adjusted amplitude and phase ratio is maintained through to the test ports. The specialist article by D. E. Bockelman, W. R. Eisenstadt: “Calibration and Verification of the Pure-Mode Vectorial Network Analyser”, IEEE Transactions on Microwave Theory and Techniques, Volume 46, No. 7, July 1998, pages 1009 to 1012 discloses a method, in which the balanced parameters are measured with a non-ideal measuring device according to U.S. Pat. No. 5,495,173 B1 and then corrected with the assumption of linear behaviour of the device under test. However, if the device under test behaves in a nonlinear manner, this method cannot be used.
US patent specifications US 2004/0196083 A1 and US 2004/0196051 A1 or respectively the German published application DE 103 57 243 A1 corresponding to US 2004/0196083 A1 provide a solution to the problem of generating the most ideal differential-mode and common-mode signals possible over a broad frequency range. FIG. 1 shows the structure of a dual-output high-frequency signal source (DOHFSS) according to this related art. A signal generator 101, which can be either an independent device or an integral component of a two-port VNA, generates a high-frequency signal. This signal is split into two paths using a signal divider 102. In one of the two paths, signal amplitude and phase can be adjusted using a vector modulator 112 via the I/Q control inputs 113, 114. In order to adjust the desired amplitude and phase difference in the reference planes 105, 106 of the DOHFSS, the incident and reflected waves are measured via coupling four-port devices 103, 104 and measuring points 107 to 110. According to US 2004/0196051 A1, the calibration of the VNA is implemented with a common-mode signal, which is generated using a signal divider. After the calibration of the VNA, the DOHFSS is calibrated in such a manner that the vectorial modulator moves in small phase increments, for example, nominal 1°, through the range from 0° to 360°. Because of the non-idealities, the actually-generated phase increments deviate from the nominal value. The actual phases are measured using the VNA and entered in the correction table. A phase value to be adjusted nominally in the vectorial modulator can then be assigned for each desired phase difference of the DOHFSS using this table.